Sea ice features a dense inner pack ice zone surrounded by a marginal ice zone (MIZ) in which the sea ice properties are modified by interaction with the ice-free open ocean. The width of the MIZ is a fundamental length scale for polar physical and biological dynamics. Several different criteria for establishing MIZ boundaries have emerged in the literature-wave penetration, floe size, sea ice concentration, etc.-and a variety of definitions for the width between the MIZ boundaries have been published. Here, three desirable mathematical properties for defining MIZ width are proposed: invariance with respect to translation and rotation on the sphere; uniqueness at every point in the MIZ; and generality, including nonconvex shapes. The previously published streamline definition is shown to satisfy all three properties, where width is defined as the arc length of a streamline through the solution to Laplaces's equation within the MIZ boundaries, while other published definitions each satisfy only one of the desired properties. When defining MIZ spatial average width from streamline results, the rationale for averaging with respect to distance along both MIZ boundaries was left implicit in prior studies. Here it is made rigorous by developing and applying the mathematics of an analytically tractable idealization of MIZ geometry-the eccentric annulus. Finally, satellite-retrieved Arctic sea ice concentrations are used to investigate how well streamline-based MIZ spatial average width is approximated by alternative definitions that lack desirable mathematical properties or local width values but offer computational efficiency.

Observations indicate that the Arctic sea ice cover is rapidly retreating while the Antarctic sea ice cover is steadily expanding. State-of-the-art climate models, by contrast, typically simulate a moderate decrease in both the Arctic and Antarctic sea ice covers. However, in each hemisphere there is a small subset of model simulations that have sea ice trends similar to the observations. Based on this, a number of recent studies have suggested that the models are consistent with the observations in each hemisphere when simulated internal climate variability is taken into account. Here sea ice changes during 1979-2013 are examined in simulations from the most recent Coupled Model Intercomparison Project (CMIP5) as well as the Community Earth System Model Large Ensemble (CESM-LE), drawing on previous work that found a close relationship in climate models between global-mean surface temperature and sea ice extent. All of the simulations with 1979-2013 Arctic sea ice retreat as fast as observations are found to have considerably more global warming than observations during this time period. Using two separate methods to estimate the sea ice retreat that would occur under the observed level of global warming in each simulation in both ensembles, it is found that simulated Arctic sea ice retreat as fast as observations would occur less than 1% of the time. This implies that the models are not consistent with the observations. In the Antarctic, simulated sea ice expansion as fast as observations is found to typically correspond with too little global warming, although these results are more equivocal. As a result, the simulations do not capture the observed asymmetry between Arctic and Antarctic sea ice trends. This suggests that the models may be getting the right sea ice trends for the wrong reasons in both polar regions.